The eccentricity of the parabola $x^2 - 4x - 4y + 4 = 0$ is

At which point does the line $x = my + \frac{a}{m}$ touch the parabola $x^2 = 4ay$?

If $m_1$ and $m_2$ are the slopes of the tangents drawn from the point $(2, 3)$ to the parabola $y^2 = 4x$,then what is the value of $\frac{1}{m_1} + \frac{1}{m_2}$?

Let one end of a focal chord of the parabola $y^{2}=16x$ be $(16, 16)$. If $P(\alpha, \beta)$ divides this focal chord internally in the ratio $5 : 2$, then the minimum value of $\alpha+\beta$ is equal to:

If the parabola $y^2 = 4ax$ passes through the point $(-3, 2)$,then the length of its latus rectum is

If $a \neq 0$ and the line $2bx + 3cy + 4d = 0$ passes through the points of intersection of the parabolas $y^2 = 4ax$ and $x^2 = 4ay$,then